How can i create n-linearly independent vectors?

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Subham Burnwal 2015-3-11

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编辑： Matt J 2015-3-11

Like 4-linearly independent vectors if n=4 as follows

a1=[1,17] , a2=[1,7] , a3=[1,1] , a4=[1,9]

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James Tursa 2015-3-11

编辑：James Tursa 2015-3-11

The simplest thing to do I suppose is just to pick off the columns of the identity matrix of the appropriate size. Do you have any other criteria that needs to be met?

I should add that your example will not work ... you can't have four linearly independent 2-element vectors, since two linearly independent 2-element vectors will span the entire space.

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Answer 1

Matt J 2015-3-11

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编辑：Matt J 2015-3-11

在 MATLAB Online 中打开

Generate any n x n nonsingular matrix, e.g.,

A = eye(n)

and take some subset of the columns.

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Answer 2

Roger Stafford 2015-3-11

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在 MATLAB Online 中打开

You can also use matlab's 'orth' function to generate linearly independent vectors which span a given space. They will in fact be orthogonal. See:

http://www.mathworks.com/help/matlab/ref/orth.html

(Note: You cannot get four linearly independent vectors from your set of two-element vectors. The maximum would be two. For example, in the vectors you give, there is the equality:

3*a1-8*a2+5*a3 = 0